Integrable one-dimensional N-component fermion model with correlated hopping and hard-core repulsion

Abstract

The N-component Bariev model for correlated hopping and a hard-core repulsion is shown to be integrable in one dimension. The solution of the model is obtained within the framework of nested Bethe ansatze. The ground state integral equations for the densities of the rapidities are derived for repulsive and attractive correlations. In zero-field and for a repulsive interaction the spin excitations are gapped and only the charge sector has a Fermi surface. The properties are then those of a one-component Luttinger liquid. The spin-gaps are gradually closed with increasing magnetic field. For an attractive interaction potential charge bound states (generalized non-local Cooper pairs) are formed and the spin excitations are gapped in zero magnetic field. The ground state properties and the critical exponents of correlation functions are discussed for both, repulsive and attractive, potentials. The string hypothesis is invoked to derive the thermodynamic Bethe ansatz equations. Some special limits of the thermodynamic equations are analyzed, e.g., the weak and strong interaction cases, and the low and high temperature limits.